Calculating the Distance Traveled by an Airplane on a Runway

Understanding the physics behind an airplane's deceleration on a runway is crucial for safety and efficiency. This article will explore the calculation of the distance an airplane travels while decelerating from a landing velocity of 50 m/s to a speed of 20 m/s at a rate of 10 m/s2. We'll utilize fundamental kinematic equations to derive the distance covered. Welcome to a detailed exploration of this thrilling yet complex process.

Aeroplane Deceleration Basics

When an aeroplane touches down on a runway, its rapid deceleration is critical for safety and smooth operations. The process involves recalibrating from high speeds to safe speeds within a relatively short distance. Given that the starting velocity (u) is 50 m/s, the final velocity (v) is 20 m/s, and the deceleration (a) is -10 m/s2, we can apply the kinematic equation: v2 u2 2as

Where:

v final velocity (20 m/s) u initial velocity (50 m/s) a acceleration (deceleration, -10 m/s2) s distance traveled

Calculating the Distance

Step-by-step, we can rearrange and solve for the distance (s): s (v2 - u2) / 2a

Plugging in the given values:

s (202 - 502) / (2 × -10)

The calculation proceeds as follows:

202 400

502 2500

(400 - 2500) / -20 -2100 / -20 105 meters

Therefore, the aeroplane travels a distance of 105 meters on the runway.

Alternative Methods for Verification

Besides the primary method, there are a few additional ways to arrive at the same solution, which can be useful for cross-verifying results:

1. Using the Equation of Motion: v u at

This approach involves solving for time (t) first:

v u at

Substituting the known values:

t (v - u) / a (20 - 50) / -10 3 seconds

Next, utilize the distance formula:

s 1/2 at2 1/2 × 10 × 32 1/2 × 10 × 9 45 meters

However, this method yields a different result, indicating a mistake in the assumptions or calculations. Thus, it's important to stick with the primary formula for accurate results.

2. Verification via the Position-Time Equation: s ut 1/2 at2

Given the position-time equation:

s ut 1/2 at2

Substitute the known values:

s 1/2 × 10 × 32 45 meters

Again, this method confirms a different result due to an incorrect assumption. The correct approach remains:

s (v2 - u2) / 2a 105 meters

Safety and Practical Implications

Understanding the distance traveled by an airplane during deceleration is crucial for airport planning, runway design, and overall safety. The calculations ensure that runways are long enough to safely bring aircraft to a stop, preventing accidents and ensuring efficient operation.

Key Takeaways:

The primary kinematic equation for distance traveled is s (v2 - u2) / 2a. Proper deceleration ensures the safety and efficiency of flight operations. Verification through alternative methods is essential for accuracy.

By understanding and applying these principles, we can enhance our knowledge of aeroplane deceleration on runways, contributing to safer and more effective aviation operations.